Class 11 Exam > Class 11 Questions > Viscous force isa)directly proportional to ar...
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Viscous force is
- a)directly proportional to area and inversely proportional to velocity gradient
- b)directly proportional to velocity gradient squared and inversely proportional to area
- c)directly proportional to area and velocity gradient
- d)directly proportional to velocity gradient and inversely proportional to area
Correct answer is option 'C'. Can you explain this answer?
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Viscous force isa)directly proportional to area and inversely proporti...
Viscous force is directly proportional to area and velocity gradient.
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Viscous force isa)directly proportional to area and inversely proporti...
The correct answer is option 'C': the viscous force is directly proportional to the area and the velocity gradient. To understand why this is the case, let's break it down into two parts: the area and the velocity gradient.
1. Viscous force and area:
The viscous force is the force that opposes the motion of an object through a fluid (such as a liquid or a gas). It arises due to the internal friction between layers of the fluid as they move relative to each other. When an object moves through a fluid, these layers of fluid near the surface of the object also move, creating a shearing effect.
- The area of the object in contact with the fluid determines the amount of fluid that is affected by the object's motion. A larger area means more fluid is involved, leading to a larger force.
2. Viscous force and velocity gradient:
The velocity gradient refers to the change in velocity of the fluid as you move away from the object's surface. It measures how quickly the velocity of the fluid changes with respect to distance.
- The greater the velocity gradient, the larger the difference in velocity between adjacent layers of fluid. This difference in velocity leads to a greater shearing effect and, consequently, a larger viscous force.
Combining the effects of the area and the velocity gradient, we can conclude that the viscous force is directly proportional to both. A larger area will increase the amount of fluid affected, while a larger velocity gradient will increase the shearing effect and the force. Therefore, option 'C' is the correct answer.
In summary, the viscous force is determined by both the area of the object in contact with the fluid and the velocity gradient, with a direct relationship to both.
1. Viscous force and area:
The viscous force is the force that opposes the motion of an object through a fluid (such as a liquid or a gas). It arises due to the internal friction between layers of the fluid as they move relative to each other. When an object moves through a fluid, these layers of fluid near the surface of the object also move, creating a shearing effect.
- The area of the object in contact with the fluid determines the amount of fluid that is affected by the object's motion. A larger area means more fluid is involved, leading to a larger force.
2. Viscous force and velocity gradient:
The velocity gradient refers to the change in velocity of the fluid as you move away from the object's surface. It measures how quickly the velocity of the fluid changes with respect to distance.
- The greater the velocity gradient, the larger the difference in velocity between adjacent layers of fluid. This difference in velocity leads to a greater shearing effect and, consequently, a larger viscous force.
Combining the effects of the area and the velocity gradient, we can conclude that the viscous force is directly proportional to both. A larger area will increase the amount of fluid affected, while a larger velocity gradient will increase the shearing effect and the force. Therefore, option 'C' is the correct answer.
In summary, the viscous force is determined by both the area of the object in contact with the fluid and the velocity gradient, with a direct relationship to both.
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